Hanover — The ECAC standings are tight and the stakes are high for the Dartmouth College men’s hockey team. The Big Green hosts Princeton tonight and No. 1 Quinnipiac tomorrow during the regular season’s final weekend. Fans are asked to leave their tennis balls at home.

Tennis balls? Well, as longtime Dartmouth fans know, a controversial tradition compels some students and townspeople to rain fuzzy orbs upon the Thompson Arena ice when Dartmouth scores its first goal against the visiting Tigers each season. The referees generally allow the initial bombardment to occur without punishment, but after that, they slap the hosts with a delay-of-game penalty each time balls fly out of the stands.

Last season, Dartmouth scored its first goal during the third minute and managed to snuff out three delay-of-game penalties during a 5-3 victory. Two years ago, it overcame three such penalties in a 4-1 triumph. During the teams’ last 12 contests at Thompson, the Big Green’s fans have seven times caused their team to skate short-handed at least once.

Tonight’s game starts at 7, and in an attempt to limit misbehavior, Dartmouth officials will not allow spectators to enter or re-enter after 7:30. The theory is that many students arrive after the first home goal and use later scores to get their tosses in.

“We’ll see people in the rink tonight who only come once a year,’’ Dartmouth Athletic Director Harry Sheehy said. “They throw and go. This thing has gotten ridiculous and I’m not proud of it.”

The tradition’s roots are murky, and it’s proven pretty much impossible for the school to stop it. However, Sheehy wants to make something crystal clear: Chuck balls on the ice tonight, and it could cost Dartmouth dearly. The Big Green (13-10-4, 9-8-3) could earn a first-round bye from next weekend’s opening playoff round or, could wind up not only having to play during that round, but do so on the road.

“I honestly think this thing has to cost us (a victory) before it will change,’’ Sheehy said. “But this would be a bad weekend for that to happen.’’

Dartmouth can finish anywhere from second place to ninth place in the 12-team ECAC standings. With variables that include his own team’s play, that of its opponents and out-of-town scoreboard watching, the last factor Big Green coach Bob Gaudet wants to add is whether home fans will cause problems.

“I’d be jacked if we scored multiple goals, but at the same time, I’d like it not to hurt us,’’ Gaudet said. “I love that our team has drawn really well all season long, but I’m not a fan of this tradition.”

Dartmouth enters the weekend tied with Ivy League champion Yale for fourth place. The ECAC’s top four finishers earn first-round byes.

The Big Green is currently a point behind third-place St. Lawrence and two behind second-place Rensselaer. Looking down, Dartmouth is one point ahead of Union, two ahead of Clarkson, three in front of Brown and four ahead of Princeton and Cornell.

Quinnipiac, 12 points ahead of RPI, has run away with its first league crown, so an upset victory tomorrow night would be a huge boost to the Big Green, which would not only earn league points but improve its potential chance of reaching the NCAA tournament for the first time since 1980.

“Motivation this time of year comes easier because the playoffs are in the air,’’ Gaudet said. “The challenge of it is fun and the hockey’s exciting and the light is at the end of the tunnel.

“The tennis ball thing is out of our control, and we’ll just play as hard as we can. We’ve got a lot on our mind right now, and we don’t want to make too much of it.”

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Notes: The No. 18 Big Green needs to earn only one point this weekend to guarantee itself at least home ice for the playoffs’ first round. … Dartmouth has lost forwards Brandon McNally and Jack Barre for the season with injuries, but Gaudet said previously injured forward Matt Lindblad played last weekend and similarly afflicted teammate Eric Robinson could dress this weekend. Defenseman Nick Lovejoy has begun skating but isn’t yet healthy enough for game action. … Although junior goaltender Cab Morris has played most of the games the last two months, Gaudet said he was leaning toward using freshman Charles Grant against Princeton. Morris was pulled from a 5-0 loss at Clarkson last weekend while Grant earned a narrow victory at St. Lawrence a night later. … Dartmouth lost one-goal games at Quinnipiac (23-4-5, 16-1-3) and Princeton (9-14-4, 7-10-3) earlier this season. … The Big Green is tied for 12th in the national Pairwise rankings, which mimic the formula used to determine the 16-team NCAA tournament’s participants. ... Following nearly two months in a pair of medical facilities, Connie Sheehy, Harry Sheehy’s wife, returned home this week after battling serious respiratory illness.